CN104699894A - JITL (just-in-time learning) based multi-model fusion modeling method adopting GPR (Gaussian process regression) - Google Patents

Abstract

The invention discloses a JITL (just-in-time learning) based multi-model fusion modeling method adopting GPR (Gaussian process regression). The method is used for a complex and changeful multi-stage chemical process and is a multi-model strategy which is continuously updated online; a Gaussian mixture model is adopted to identify different stages of the process, and a self-adaptive learning method is adopted to continuously update an established GPR model; when new data arrive, partially similar data are selected based on Euclidean distance and angle principle at each stage and used for establishing a partial GPR model; finally, new data obtained through calculation belong to posterior probability of each stage, and the partial model is subjected to fusion output. According to the method, key variables can be predicated accurately, so that the product quality is improved, and the production cost is reduced.

Description

Gaussian process based on real-time learning returns multi-model Fusion Modeling Method

Technical field

The Gaussian process that the present invention relates to based on real-time learning returns multi-model Fusion Modeling Method, belongs to complex industrial process modeling and hard measurement field.

Background technology

At present, the complicacy of chemical process increases day by day, is also improving constantly the requirement of product quality, and modern industry often needs the supervisory system of equipping some advanced persons.But because the sensor of some Key Quality variable is expensive, poor reliability or there is the shortcomings such as very large measurement delay, the process variable causing some important can not be measured in real time effectively.

In order to address these problems, soft-measuring technique receives in industrial process field and pays close attention to more and more widely.More than ten years in the past, the soft sensor modeling technology based on data-driven obtains extensive research, for improving the quality of product, reduces the impact on environment.The method of some conventional linear regressions is as offset minimum binary (partial least squares, PLS), principal component analysis (PCA) (principal component analysis, PCA) etc. can process the linear relationship between input variable and output variable well.But, nonlinear relation is usually presented between input and output, linear modeling approach is no longer applicable, non-linear modeling method is as artificial neural network (artificial neural networks, ANN), support vector machine (support vector machine, SVM), least square method supporting vector machine (least squares support vector machine, LS-SVM) can obtain good precision of prediction.

Although these methods can obtain good overall Generalization Capability, industrial process usually present the multistage, time become dynamic perfromance, prediction effect often can not be guaranteed.Gaussian process returns (Gaussian process regression, GPR) partial model can be set up based on similarity criterion, as a kind of nonparametric density estimation, GPR model not only can provide predicted value, can also obtain the trust value of predicted value to model.Therefore, GPR is selected to set up soft-sensing model.

Chemical process presents serious non-linear, time variation and multistage negotiation.Be directed to multistage property, by the division to each operator scheme, different partial models can be set up, be described in the dynamic perfromance in different operating stage.Although effectively can divide the different phase of chemical process, in each operational phase, the time variation of process and device characteristics may change, and these can make the estimated performance of soft-sensing model worsen.In order to avoid the reduction of precision of prediction, need to constantly update on-line prediction model.

A kind of method based on real-time learning (just-in-time learning, JITL) can the time variation of processing procedure and non-linear well, improves the performance of soft-sensing model.Different from the world model that classic method is set up, the model that JITL method is set up has local dynamic station structure.Traditional world model is that off-line is set up, and is online foundation based on the partial model of JITL method, and this model can tracing process is current better state.Meanwhile, what set up due to JITL is partial model, and therefore it can processing procedure better non-linear.

Summary of the invention

Non-linear, the time variation being directed to that chemical process presents and multistage row, product quality often can not be guaranteed, in order to improve the quality of product, the invention provides a kind of multi-model can measuring multistage chemical process product quality in real time and merging soft-measuring modeling method.

The stage different to chemical process by GMM carries out identification, then divides set of metadata of similar data to set up local PCA-GPR model in the specific stage by JITL selection portion.Finally, for the different operational phases, merge according to the output of posterior probability to different partial model that identification obtains, realize the On-line Estimation to chemical process product quality, thus improve output, reduce production cost.

The object of the invention is to be achieved through the following technical solutions:

Gaussian process based on practice study returns multi-model Fusion Modeling Method, described method comprises following process: the chemical process being directed to multistage negotiation complicated and changeable, with gauss hybrid models, identification is carried out to the different phase of process, and adopt a kind of self-adaptation real-time learning method, constantly update the Gaussian process regression model set up.

When new data arrive, in each different stage, based on data like Euclidean distance and the phase-splitting of angle principle selection portion, for setting up the Gaussian process regression model of local.

The new data membership that final basis calculates, in the posterior probability of each different phase, carries out fusion to partial model and exports, can carry out accurately predicting, thus improve the quality of products to key variables, reduce production cost.

Accompanying drawing explanation

Fig. 1 is the online soft sensor multi-model integration modeling process flow diagram based on GMM and JITL-GPR;

CPU is consuming time for Fig. 2 different proportion;

The RMSE of Fig. 3 different proportion prediction;

What Fig. 4 test data was under the jurisdiction of each different operating stage is subordinate to angle value;

Fig. 5 is ratio data on-line prediction result figure when being 70%;

Embodiment

Shown in Fig. 1, the present invention is further described:

For common chemical process---TE process.Experimental data comes from TE process, predicts the content of composition A in prediction product stream.

Step 1: collect inputoutput data composition historical training dataset.

Step 2: utilize these training datas to estimate to obtain the parameter of gauss hybrid models (Gaussian mixture model, GMM).Then complete input and output training data is assigned to the different operational phases.Described GMM algorithm is:

GMM is mixed by multiple gauss component, about data X ∈ R ^{n × m}probability density function can be expressed as:

$p\left(X\right|{\mathrm{\Θ}}_{\mathrm{GM}})=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\π}}_{k}N\left(X\right|{\mathrm{\μ}}_k,{\mathrm{\σ}}_k^2)---\left(1\right)$

Wherein, m is the number of process variable, and n is the size of sample data. the parameter of gauss hybrid models, wherein μ _k, and π _krepresent the average of a kth gauss component, covariance and weights respectively.Meanwhile, parameter π _kmeet with 0≤π _k≤ 1.

In formula (1) represent multivariate Gaussian probability density function:

$N\left(x_i\right|{\mathrm{\μ}}_k,{\mathrm{\σ}}_k^2)=\frac{\exp \{-\frac{1}{2}{(x_i-{\mathrm{\μ}}_k)}^T{\left({\mathrm{\σ}}_k^2\right)}^{-1}(x_i-{\mathrm{\μ}}_k)\}}{{\left(2\mathrm{\π}\right)}^{1/2}{\left|{\mathrm{\σ}}_k^2\right|}^{1/2}}---\left(2\right)$

By the parameter of expectation-maximization algorithm (expectation-maximization, EM) estimation model, solution procedure is divided into two steps of continuous iteration:

E-walks: according to existing observation data and the probability γ by a kth composition generation _k(x _i), obtain Q function:

$Q\left({\mathrm{\Θ}}_{\mathrm{GM}}\right)=\underset{i-1}{\overset{n}{\mathrm{\Σ}}}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\γ}}_k\left(x_i\right)[\ln {\mathrm{\π}}_k-\ln {\mathrm{\σ}}_k-\frac{{(x_i-{\mathrm{\μ}}_k)}^T(x_i-{\mathrm{\μ}}_k)}{2{\mathrm{\σ}}_k^2}]---\left(3\right)$

M-walks: solve the partial derivative of Q function to each parameter, can obtain new estimates of parameters:

$\left\{\begin{array}{c}{\mathrm{\μ}}_k=\frac{1}{N_k}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\γ}}_k\left(x_i\right)x_i\\ {\mathrm{\σ}}_k^2=\frac{1}{N_k}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\γ}}_k\left(x_i\right)(x_i-{\mathrm{\μ}}_k){(x_i-{\mathrm{\μ}}_k)}^T\\ {\mathrm{\π}}_k=\frac{N_k}{n}\\ N_k=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\γ}}_k\left(x_i\right)\end{array}\right.---\left(4\right)$

According to the parameter estimating the GMM obtained, for new input x ^*, its posterior probability about each gauss component can be tried to achieve by through type (5):

${\mathrm{\γ}}_k\left(x^{*}\right)=\frac{{\mathrm{\π}}_{k}N\left(x^{*}\right|{\mathrm{\μ}}_k,{\mathrm{\σ}}_k^2)}{\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\π}}_{k}N\left(x^{*}\right|{\mathrm{\μ}}_k,{\mathrm{\σ}}_k^2)}---\left(5\right)$

Step 3: the different operating stage obtained according to step 2 identification, the subdata base that correspondence establishment is different.When a new data arrives, according to this new data membership in the posterior probability of each subdata base, the subdata base that corresponding posterior probability is maximum upgrades.

For the different operational phases, in order to carry out dimensionality reduction to process variable, solving correlativity very strong between different variable, utilizing traditional PCA method process variable analysis to be obtained to the score variable of pca model.PCA algorithm is:

Given training data X ∈ R ^{n × m}, m is the dimension of process variable, and n is the number of training data.PCA realizes on the covariance matrix basis of X.Generally, the Method Modeling pca model of svd (singular value decomposition, SVD) can be passed through.Suppose that pca model has q major component, X can be broken down into following form:

$X={\mathrm{TP}}^T+\tilde{T}{\tilde{P}}^T={\mathrm{TP}}^T+E---\left(6\right)$

In formula, T ∈ R ^{n × q}with the score matrix of major component subspace and residual error subspace respectively, P ∈ R ^{m × q}with be the corresponding loading matrix in major component subspace and residual error subspace, E is residual matrix.

When needs carry out prediction output to input, do not need to know which operational phase is these new data be specifically under the jurisdiction of, select the most similar data to set up the local PCA-GPR model of each operational phase with JITL in each operational phase.JITL algorithm is as follows:

Step1: calculate x _qand x _ibetween Euclidean distance and angle:

d(x _q,x _i)＝||x _q,x _i|| ₂，i＝1,...,N (7)

$\begin{array}{c}\cos \left({\mathrm{\θ}}_i\right)=\frac{\mathrm{\Δ}{x}_q\mathrm{\Δ}{x}_i^T}{{\left|\right|\mathrm{\Δ}{x}_q\left|\right|}_2\·{\left|\right|\mathrm{\Δ}{x}_i\left|\right|}_2},i=1,...,N\\ \mathrm{\Δ}{x}_q=x_q-x_{q-1},\mathrm{\Δ}{x}_i=x_i-x_{i-1}\end{array}---\left(8\right)$

If cos is (θ _i)>=0, calculates similarity coefficient s _i:

$s_i=\mathrm{\γ}\sqrt{e^{-d_i^2}}+(1-\mathrm{\γ})\cos \left({\mathrm{\θ}}_i\right)---\left(9\right)$

In formula, γ is the weight coefficient between 0 and 1, if cos is (θ _i) <0, abandon data (x _i, y _i).The s calculated _ialso between zero and one, s _imore close to 1, x _iwith x _qsimilarity higher.

To all similarity coefficient s calculating gained _icarry out descending sort, when setting up partial model, the data that before only selecting, L similarity coefficient is larger.In order to select the modeling data of proper ratio, be directed to TE chemical process, ratio data is selected to increase to 100% gradually from 10%, and finally obtaining best ratio data is 70%.When JITL carries out data selection, under different ratios, the CPU precision with predicting consuming time as shown in Figures 2 and 3.

According to the local GPR model that the data of JITL selection are set up be:

Given training sample set X ∈ R ^{d × N}with y ∈ R ⁿ, wherein X={x _i∈ R ^d} _i=1...N, y={y _i∈ R} _i=1...Nrepresent the input and output data of D dimension respectively.Relation between input and output is produced by formula (10):

y＝f(x)+ε (10)

Wherein f is unknown functional form, and ε is average is 0, and variance is gaussian noise.For a new input x ^*, corresponding probabilistic forecasting exports y ^*also meet Gaussian distribution, its average and variance are such as formula shown in (11) and (12):

y ^*(x ^*)＝c ^T(x ^*)C ^-1y (11)

${\mathrm{\&sigma;}}_{y^{*}}^2\left(x^{*}\right)=c(x^{*},x^{*})-c^T\left(x^{*}\right)C^{-1}c\left(x^{*}\right)---\left(12\right)$

C (x in formula ^*)=[c (x ^*, x ₁) ..., c (x ^*, x _n)] ^tit is the covariance matrix between training data and test data. be the covariance matrix between training data, I is the unit matrix of N × N dimension.C (x ^*, x ^*) be the autocovariance of test data.

GPR can select different covariance function c (x _i, x _j) produce covariance matrix Σ, as long as the covariance function selected can ensure that the covariance matrix produced meets the relation of non-negative positive definite.Select Gauss's covariance function herein:

$c(x_i,x_j)=\mathrm{v\; exp}[-\frac{1}{2}\underset{d=1}{\overset{D}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_d{(x_i^d-x_j^d)}^2]---\left(13\right)$

In formula, v controls measuring of covariance, ω _drepresent each composition x ^drelative importance.

To the unknown parameter v in formula (4), ω ₁..., ω _dand Gaussian noise variance estimation, generally the simplest method obtains parameter by Maximum-likelihood estimation exactly $\mathrm{\&theta;}=[v,{\mathrm{\&sigma;}}_n^2,{\mathrm{\&omega;}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&omega;}}_D].$

$L\left(\mathrm{\&theta;}\right)=-\frac{1}{2}\log \left(\det \left(C\right)\right)-\frac{1}{2}{y}^T{C}^{-1}y-\frac{N}{2}\log \left(2\mathrm{\&pi;}\right)---\left(14\right)$

In order to try to achieve the value of parameter θ, first parameter θ is set to the random value in a zone of reasonableness, then by the parameter that method of conjugate gradient is optimized.After obtaining optimized parameter θ, for test sample book x ^*, the output valve of GPR model can be estimated by formula (11) and (12).

Step 6: the angle value (as shown in Figure 4) that is subordinate to that the partial model of each operational phase set up step 5 utilizes the test data required by formula (5) to be under the jurisdiction of each different operating stage is carried out fusion and obtained Global model prediction:

$y^{*}\left(x^{*}\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{y}_k^{*}\left(x^{*}\right){\mathrm{\&gamma;}}_k\left(x^{*}\right)---\left(15\right)$

The output of Global model prediction is predicting the outcome of the content of composition A in product stream.

The content of Fig. 5 is ratio data when being 70% in on-line prediction product stream composition A and actual value matched curve, and compare with the soft-sensing model that LSSVM sets up.As seen from the figure, the Gaussian process based on practice study returns the content that multi-model integration modeling can predict composition A in product stream effectively.

Claims (2)

1. the Gaussian process based on real-time learning returns multi-model Fusion Modeling Method, and it is characterized in that, the method step is:

Step 1: collect inputoutput data composition historical training dataset

Step 2: utilize these training datas to estimate to obtain the parameter of gauss hybrid models (Gaussian mixture model, GMM).Then complete input and output training data is assigned to the different operational phases.Described GMM algorithm is:

GMM is mixed by multiple gauss component, about data X ∈ R ^{n × m}probability density function can be expressed as:

$p\left(X\right|{\mathrm{\&Theta;}}_{\mathrm{GM}})=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}_{k}N\left(X\right|{\mathrm{\&mu;}}_k,{\mathrm{\&sigma;}}_k^2)---\left(1\right)$

Wherein, m is the number of process variable, and n is the size of sample data. the parameter of gauss hybrid models, wherein μ _k, and π _krepresent the average of a kth gauss component, covariance and weights respectively.Meanwhile, parameter π _kmeet with 0≤π _k≤ 1.In formula (1) represent multivariate Gaussian probability density function:

$N\left(x_i\right|{\mathrm{\&mu;}}_k,{\mathrm{\&sigma;}}_k^2)=\frac{\exp \{-\frac{1}{2}{(x_i-{\mathrm{\&mu;}}_k)}^T{\left({\mathrm{\&sigma;}}_k^2\right)}^{-1}(x_i-{\mathrm{\&mu;}}_k)\}}{{\left(2\mathrm{\&pi;}\right)}^{d/2}|{\mathrm{\&sigma;}}_k^2{|}^{1/2}}---\left(2\right)$

By expectation-maximization algorithm (expectation-maximization, EM) parameter of estimation model, solution procedure is divided into two steps of continuous iteration: E-walks: estimate missing data γ according to existing observation data with by the general existing model of a kth composition generation _k(x _i), obtain Q function:

$Q\left({\mathrm{\&Theta;}}_{\mathrm{GM}}\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_k\left(x_i\right)[\ln {\mathrm{\&pi;}}_k-\ln {\mathrm{\&sigma;}}_k-\frac{{(x_i-{\mathrm{\&mu;}}_k)}^T(x_i-{\mathrm{\&mu;}}_k)}{2{\mathrm{\&sigma;}}_k^2}]---\left(3\right)$

M-walks: solve the partial derivative of Q function to each parameter, can obtain new estimates of parameters:

$\left\{\begin{array}{c}{\mathrm{\&mu;}}_k=\frac{1}{N_k}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_k\left(x_i\right)x_i\\ {\mathrm{\&sigma;}}_k^2=\frac{1}{N_k}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_k\left(x_i\right)(x_i-{\mathrm{\&mu;}}_k){(x_i-{\mathrm{\&mu;}}_k)}^T\\ {\mathrm{\&pi;}}_k=\frac{N_k}{n}\\ N_k=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_k\left(x_i\right)\end{array}\right.---\left(4\right)$

According to the parameter estimating the GMM obtained, for new input x ^*, its posterior probability about each gauss component can be tried to achieve by through type (5):

${\mathrm{\&gamma;}}_k\left(x^{*}\right)=\frac{{\mathrm{\&pi;}}_{k}N\left(x^{*}\right|{\mathrm{\&mu;}}_k,{\mathrm{\&sigma;}}_k^2)}{\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&pi;}}_{k}N\left(x^{*}\right|{\mathrm{\&mu;}}_k,{\mathrm{\&sigma;}}_k^2)}---\left(5\right)$

Step 3: the different operating stage obtained according to step 2 identification, the subdata base that correspondence establishment is different.When a new data arrives, according to this new data membership in the posterior probability of each subdata base, the subdata base that corresponding posterior probability is maximum upgrades.

Step 4: for the different operational phases, in order to carry out dimensionality reduction to process variable, solves correlativity very strong between different variable, utilizes traditional PCA method process variable analysis to be obtained to the score variable of pca model.PCA algorithm is:

Given training data X ∈ R ^{n × m}, m is the dimension of process variable, and n is the number of training data.PCA realizes on the covariance matrix basis of X.Generally, the Method Modeling pca model of svd (singular value decomposition, SVD) can be passed through.Suppose that pca model has q major component, X can be broken down into following form ^[11]:

$X={\mathrm{TP}}^T+\tilde{T}{\tilde{P}}^T={\mathrm{TP}}^T+E---\left(6\right)$ In formula, T ∈ R ^{n × q}with the score matrix of major component subspace and residual error subspace respectively, P ∈ R ^{m × q}with be the corresponding loading matrix in major component subspace and residual error subspace, E is residual matrix.

Step 5: when needs carry out prediction output to input, do not need to know which operational phase is these new data be specifically under the jurisdiction of, select the most similar data to set up the local PCA-GPR model of each operational phase with JITL in each operational phase.

JITL algorithm is as follows: Step1: calculate x _qand x _ibetween Euclidean distance and angle:

$d(x_q,x_i)=\left|\right|x_q,x_i{\left|\right|}_2,i=1,...,N---\left(7\right)$

$\cos \left({\mathrm{\&theta;}}_i\right)=\frac{\mathrm{\&Delta;}{x}_q\mathrm{\&Delta;T}{x}_i^T}{\left|\right|\mathrm{\&Delta;}{x}_q{\left|\right|}_2\&CenterDot;\left|\right|\mathrm{\&Delta;}{x}_i|{|}_2},i=1,...,N---\left(8\right)$

Δx _q＝x _q-x _q-1,Δx _i＝x _i-x _i-1

If cos is (θ _i)>=0, calculates similarity coefficient s _i:

$s_i=\mathrm{\&gamma;}\sqrt{e^{-d_i^2}}+(1-\mathrm{\&gamma;})\cos \left({\mathrm{\&theta;}}_i\right)---\left(9\right)$

In formula, γ is the weight coefficient between 0 and 1, if cos is (θ _i) <0, abandon data (x _i, y _i).The s calculated _ialso between zero and one, s _imore close to 1, x _iwith x _qsimilarity higher.

Step2: to all similarity coefficient s calculating gained _icarry out descending sort, when setting up partial model, the data that before only selecting, L similarity coefficient is larger.In order to select the modeling data of proper ratio, be directed to TE chemical process, ratio data is selected to increase to 100% gradually from 10%, and finally obtaining best ratio data is 70%.

According to the local GPR model that the data of JITL selection are set up be:

Given training sample set X ∈ R ^{d × N}with y ∈ R ⁿ, wherein X={x _i∈ R ^d} _{i=1 ... N}, y={y _i∈ R} _{i=1 ... N}represent the input and output data of D dimension respectively.Relation between input and output is produced by formula (10):

y＝f(x)+ε (10)

Wherein f is unknown functional form, and ε is average is 0, and variance is gaussian noise.For a new input x ^*, corresponding probabilistic forecasting exports y ^*also meet Gaussian distribution, its average and variance are such as formula shown in (11) and (12):

y ^*(x ^*)＝c ^T(x ^*)C ^-1y (11)

${\mathrm{\&sigma;}}_{y^{*}}^2\left(x^{*}\right)=c(x^{*},x^{*})-c^T\left(x^{*}\right)C^{-1}c\left(x^{*}\right)---\left(12\right)$

C (x in formula ^*)=[c (x ^*, x ₁) ..., c (x ^*, x _n)] ^tit is the covariance matrix between training data and test data. be the covariance matrix between training data, I is the unit matrix of N × N dimension.C (x ^*, x ^*) be the autocovariance of test data.

GPR can select different covariance function c (x _i, x _j) produce covariance matrix Σ, as long as the covariance function selected can ensure that the covariance matrix produced meets the relation of non-negative positive definite.Select Gauss's covariance function herein:

$c(x_i,x_j)=\mathrm{vexp}[-\frac{1}{2}\underset{d=1}{\overset{D}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_d{(x_i^d-x_j^d)}^2]---\left(13\right)$

In formula, v controls measuring of covariance, ω _drepresent each composition x ^drelative importance.

To the unknown parameter v in formula (4), ω ₁..., ω _dand Gaussian noise variance estimation, generally the simplest method obtains parameter by Maximum-likelihood estimation exactly $\mathrm{\&theta;}=[v,{\mathrm{\&sigma;}}_n^2,{\mathrm{\&omega;}}_1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&omega;}}_D].$

$L\left(\mathrm{\&theta;}\right)=-\frac{1}{2}\log \left(\det \left(C\right)\right)-\frac{1}{2}{y}^T{C}^{-1}y-\frac{N}{2}\log \left(2\mathrm{\&pi;}\right)---\left(14\right)$

In order to try to achieve the value of parameter θ, first parameter θ is set to the random value in a zone of reasonableness, then by the parameter that method of conjugate gradient is optimized.After obtaining optimized parameter θ, for test sample book x ^*, the output valve of GPR model can be estimated by formula (11) and (12).

Step 6: utilize formula (5) to carry out fusion to the partial model of each operational phase that step 5 is set up and obtain Global model prediction:

$y^{*}\left(x^{*}\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{y}_k^{*}\left(x^{*}\right){\mathrm{\&gamma;}}_k\left(x^{*}\right)---\left(15\right)$

2. the Gaussian process based on real-time learning according to claim 1 returns multi-model Fusion Modeling Method, it is characterized in that, when needing to predict new data soft-sensing model, in real time model is upgraded, and do not need the operation model of knowing that active procedure is concrete.